双组分Camassa-Holm浅水系统的非均匀依赖性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-07-04 DOI:10.1016/j.jmaa.2025.129853

Jinlu Li , Yanghai Yu , Weipeng Zhu

引用次数: 0

摘要

本文考虑直线上双分量Camassa-Holm方程的初值问题。我们给出了一种研究初始数据非一致依赖的新方法。我们用s>；3/2证明了该问题的解映射在Sobolev空间Hs(R)×Hs−1(R)中不一致连续。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Non-uniform dependence for the two-component Camassa-Holm shallow water system

In this paper, we consider the initial value problem to the two-component Camassa-Holm equation on the line. We give a new approach to studying non-uniform dependence on initial data. We prove that the solution map of this problem is not uniformly continuous in Sobolev spaces

H^{s} (R) \times H^{s - 1} (R)

with

s > 3 / 2

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.